Elimination Theory for Solvable Polynomial Algebras and Their Free Modules

2018/12/30 by Huishi Li, Li, Huishi
Computer Science · Mathematics · #68W30 (16Z05) #Advanced Differential Equations and Dynamical Systems #Commutative Algebra and Its Applications #FOS: Mathematics #Polynomial and algebraic computation #Primary 13P10 #Rings and Algebras (math.RA) #Secondary 16W70

paper · pdf · doi:10.48550/arxiv.1812.11491

openalex publication_date 2018/12/30 · openalex created_date 2019/01/11 · openalex updated_date 2026/07/28

Abstract

Let K be a field, and A=K[a₁,… ,a_n] a solvable polynomial algebra in the sense of [K-RW, \it J. Symbolic Comput., 9(1990), 1--26]. Based on the Gröbner basis theory for A and for free modules over A, an elimination theory for left ideals of A and an elimination theory for submodules of free A-modules are established.

Related

• A Constructive Characterization of Solvable Polynomial Algebras
• Notes on Gröbner Bases and Free Resolutions of Modules over Solvable Polynomial Algebras
• An Elimination Lemma for Algebras with PBW Bases
• On Computing the Elimination Ideal Using Resultants with Applications to Gröbner Bases
• Computation of Minimal Filtered Free Resolutions over ℕ-Filtered Solvable Polynomial Algebras